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Goffredo Chirco

Publications and source records attributed to Goffredo Chirco.

32 records · Page 2Linked to original sources
arXiv2018

Fisher Metric, Geometric Entanglement and Spin Networks

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of non-local correlations between two non-adjacent regions of a generic spin network graph characterized by the bipartite unfolding of an Intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and non-local level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

gr-qc↗
arXiv2017

Ryu-Takayanagi Formula for Symmetric Random Tensor Networks

We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the Rènyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.

hep-th↗
arXiv2017

On the fate of the Hoop Conjecture in quantum gravity

We consider a closed region $R$ of 3d quantum space modeled by $SU(2)$ spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary $\partial R$ and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interprete such phenomenon as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the formation of a horizon in General Relativity.

gr-qc↗
arXiv2017

Thermally correlated states in Loop Quantum Gravity

We study a class of loop-quantum-gravity states characterized by (ultra-local) thermal correlations that reproduce some features of the ultraviolet structure of the perturbative quantum field theory vacuum. In particular, they satisfy an analog of the Bisognano-Wichmann theorem. These states are peaked on the intrinsic geometry and admit a semiclassical interpretation. We study how the correlations extend on the spin-network beyond the ultra local limit.

gr-qc↗
arXiv2016

Typicality in spin network states of quantum geometry

In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network; however, they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background-independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the proof that in that regime there are certain (local) properties of quantum geometry which are "universal". Such a set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound.

gr-qc↗
arXiv2016

Statistical mechanics of covariant systems with multi-fingered time

Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the Jüttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.

gr-qc↗
arXiv2016

Statistical mechanics of reparametrization-invariant systems. It takes three to tango

It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of these notions can be defined, sufficient for statistical mechanics. We focus on reparametrization-invariant systems without additional gauges. The key is to reconstruct statistical mechanics from the ergodic theorem. We find that a suitable split of the system into two non interacting components is sufficient for generalizing statistical mechanics. While equilibrium acquires sense only when the system admits a suitable split into three weakly interacting components ---roughly: a clock and two systems among which a generalization of energy is equi-partitioned. This allows the application of statistical mechanics and thermodynamics as an additivity condition of such generalized energy.

gr-qc↗
arXiv2014

Spacetime thermodynamics without hidden degrees of freedom

A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.

gr-qc↗
arXiv2013

Coupling and thermal equilibrium in general-covariant systems

A fully general-covariant formulation of statistical mechanics is still lacking. We take a step toward this theory by studying the meaning of statistical equilibrium for coupled, parametrized systems. We discuss how to couple parametrized systems. We express the thermalization hypothesis in a general-covariant context. This takes the form of vanishing of information flux. An interesting relation emerges between thermal equilibrium and gauge.

gr-qc↗
arXiv2011

Higher Curvature Gravity and the Holographic fluid dual to flat spacetime

Recent works have demonstrated that one can construct a (d+2) dimensional solution of the vacuum Einstein equations that is dual to a (d+1) dimensional fluid satisfying the incompressible Navier-Stokes equations. In one important example, the fluid lives on a fixed timelike surface in the flat Rindler spacetime associated with an accelerated observer. In this paper, we show that the shear viscosity to entropy density ratio of the fluid takes the universal value 1/4πin a wide class of higher curvature generalizations to Einstein gravity. Unlike the fluid dual to asymptotically anti-de Sitter spacetimes, here the choice of gravitational dynamics only affects the second order transport coefficients. We explicitly calculate these in five-dimensional Einstein-Gauss-Bonnet gravity and discuss the implications of our results.

hep-th↗
arXiv2011

Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories

We derive the equations of motion for Palatini F(R) gravity by applying an entropy balance law T dS= δQ+δN to the local Rindler wedge that can be constructed at each point of spacetime. Unlike previous results for metric F(R), there is no bulk viscosity term in the irreversible flux δN. Both theories are equivalent to particular cases of Brans-Dicke scalar-tensor gravity. We show that the thermodynamical approach can be used ab initio also for this class of gravitational theories and it is able to provide both the metric and scalar equations of motion. In this case, the presence of an additional scalar degree of freedom and the requirement for it to be dynamical naturally imply a separate contribution from the scalar field to the heat flux δQ. Therefore, the gravitational flux previously associated to a bulk viscosity term in metric F(R) turns out to be actually part of the reversible thermodynamics. Hence we conjecture that only the shear viscosity associated with Hartle-Hawking dissipation should be associated with irreversible thermodynamics.

gr-qc↗
arXiv2010

Gedanken experiments on nearly extremal black holes and the Third Law

A gedanken experiment in which a black hole is pushed to spin at its maximal rate by tossing into it a test body is considered. After demonstrating that this is kinematically possible for a test body made of reasonable matter, we focus on its implications for black hole thermodynamics and the apparent violation of the third law (unattainability of the extremal black hole). We argue that this is not an actual violation, due to subtleties in the absorption process of the test body by the black hole, which are not captured by the purely kinematic considerations.

gr-qc↗
arXiv2010

The universal viscosity to entropy density ratio from entanglement

We present evidence that the universal Kovtun-Son-Starinets shear viscosity to entropy density ratio of 1/4πcan be associated with a Rindler causal horizon in flat spacetime. Since there is no known holographic (gauge/gravity) duality for this spacetime, a natural microscopic explanation for this viscosity is in the peculiar properties of quantum entanglement. In particular, it is well-known that the Minkowski vacuum state is a thermal state and carries an area entanglement entropy density in the Rindler spacetime. Based on the fluctuation-dissipation theorem, we expect a similar notion of viscosity arising from vacuum fluctuations. Therefore, we propose a holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk. We calculate this viscosity assuming a minimally coupled scalar field theory and find that the ratio with respect to the entanglement entropy density is exactly 1/4πin four dimensions. The issues that arise in extending this result to non-minimally coupled scalar fields, higher spins, and higher dimensions provide interesting hints about the relationship between entanglement entropy and black hole entropy.

hep-th↗